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Unformatted text preview: ) , w ( ) = ( v ( )) . Make sure that your conditions are satised at least for one nonzero transfer function G = G ( s ). Problem 4.3 For the pendulum equation y ( t ) + y + sin ( y ) = , nd a single continuously dierentiable Lyapunov function V = V ( y, y ) that yields the maximal region of attraction of the equilibrium y = y = 0. (In other words, the level set x R 2 : V ( { x ) < 1 } schould be a union of disjoint open sets, one of which is the attractor of the zero equilibrium, and V ( y ( t ) , y ( t )) schould have negative derivative at all points of except the origin.)...
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 Spring '09
 AlexandreMegretski
 Dynamics

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